Quantum Thouless-Anderson-Palmer equations for glassy systems

We derive Thouless-Anderson-Palmer (TAP) equations for quantum disordered systems. We apply them to the study of the paramagnetic and glassy phases of a quantum extension of the spherical p spin-glass model. We generalize several useful quantities (complexity, threshold level, etc.) and various ideas (configurational entropy crisis, etc.) that have been developed within the classical TAP approach to quantum systems. The analysis of the quantum TAP equations allows us to show that the phase diagram (temperature versus quantum parameter) of the p spin-glass model should be generic. In particular, we argue that a crossover from a second-order thermodynamic transition close to the classical critical point to a first-order thermodynamic transition close to the quantum critical point is to be expected in a large class of systems.